Heat oven to 450°F. Remove giblets and neck from chicken; save for another use or discard. Rinse chicken and pat dry. Place on top of a wire rack in a roasting pan.
Grate the zest from the lemon. Cut lemon in half, juice one half of the lemon. In a small bowl, combine 1 tablespoon of the lemon juice, 1/2 teaspoon of the lemon zest, feta cheese, oregano, garlic salt and pepper. Stir to combine. Slip your fingers under the skin of the chicken to loosen slightly. Stuff the lemon-cheese mixture under the skin, trying to spread as evenly as possible. Place remaining lemon half and the onion in the cavity of the bird. Tie the legs together with kitchen twine, if desired. Pour chicken broth into pan.
Roast chicken at 450°F for 1 hour, 15 minutes or until an instant-read thermometer inserted in the thickest part of the thigh registers 170°F. Remove chicken to a platter and let rest, tented with foil, for 10 minutes. Pour pan drippings into a fat separator. Pour juices into a serving bowl; discard the fat left behind. Slice chicken; serve with pan juices on the side.